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<title>Problem 2253. -- [2010 Beijing wc]纸箱堆叠  -- 衡阳八中OJ离线版-2012-02-29</title><center><h2>2253: [2010 Beijing wc]纸箱堆叠 </h2><span class=green>Time Limit: </span>30 Sec&nbsp;&nbsp;<span class=green>Memory Limit: </span>256 MB<br><span class=green>Submit: </span>40&nbsp;&nbsp;<span class=green>Solved: </span>19<br>[<a href='submitpage.php?id=2253'>Submit</a>][<a href='problemstatus.php?id=2253'>Status</a>][<a href='bbs.php?id=2253'>Discuss</a>]</center><h2>Description</h2><div class=content><p>P 工厂是一个生产纸箱的工厂。纸箱生产线在人工输入三个参数 n p a , , 之后，<br />
即可自动化生产三边边长为</p>
<p>(a mod P,a^2 mod p,a^3 mod P)<br />
(a^4 mod p,a^5 mod p,a^6 mod P)<br />
....<br />
(a^(3n-2) mod p,a^(3n-1) mod p,a^(3n) mod p)</p>
<p>的n个纸箱。在运输这些纸箱时，为了节约空间，必须将它们嵌套堆叠起来。<br />
一个纸箱可以嵌套堆叠进另一个纸箱当且仅当它的最短边、次短边和最长边<br />
长度分别严格小于另一个纸箱的最短边、次短边和最长边长度。这里不考虑<br />
任何旋转后在对角线方向的嵌套堆叠。 <br />
你的任务是找出这n个纸箱中数量最多的一个子集，使得它们两两之间都可<br />
嵌套堆叠起来。</p></div><h2>Input</h2><div class=content><p>输入文件的第一行三个整数，分别代表&nbsp;a,p,n&nbsp;&nbsp;<br />
</p></div><h2>Output</h2><div class=content><p>&nbsp;<br />
输出文件仅包含一个整数，代表数量最多的可嵌套堆叠起来的纸箱的个数。</p></div><h2>Sample Input</h2>
			<div class=content><span class=sampledata> 10 17 4 <br />
</span></div><h2>Sample Output</h2>
			<div class=content><span class=sampledata> <br />
2 <br />
【样例说明】 <br />
生产出的纸箱的三边长为(10, 15, 14), (4, 6, 9) , (5, 16, 7), (2, 3, 13)。其中只有<br />
(4, 6, 9)可堆叠进(5, 16, 7)，故答案为 2。<br />
2<=P<=2000000000,1<=a<=p-1,a^k mod p<>0,ap<=2000000000,1<=N<=50000 </span></div><h2>HINT</h2>
			<div class=content><p></p></div><h2>Source</h2>
			<div class=content><p><a href='problemset.html?search='></a></p></div><center>[<a href='submitpage.php?id=2253'>Submit</a>][<a href='problemstatus.php?id=2253'>Status</a>][<a href='bbs.php?id=2253'>Discuss</a>]</center>﻿<br>

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